%I A095989
%S A095989 1,2,8,48,368,3376,35824,430512,5773936,85482032,1384936688,24380214960,
%T A095989 463522810736,9468048895792,206831329017328,4812581925690288,
%U A095989 118843801816575088,3104590192664327216,85544737118902122224
%N A095989 INVERTi transform applied to the ordered Bell numbers.
%C A095989 A set composition of n is an ordered sequence [S_1, S_2, ..., S_k] where 
               S_i subset of [n] all disjoint and the union of all S_i is [n] (see 
               A000670). A set composition is atomic if S_1 union ... union S_j 
               does not equal [r] for any r<n and j<k. a(n) is the number of atomic 
               set compositions.
%C A095989 A preference function of n is a word of length n where all the numbers 
               1 through k occur at least once for some k<=n (see A000670). A preference 
               function is atomic if no strict leading subword contains the only 
               occurrences in the word of the letters 1 through j<k. a(n) is the 
               number of atomic preference functions.
%F A095989 G.f.: 1-1/sum( A000670(k)*q^k, k >= 0)
%e A095989 atomic set compositions a(1)=1: [{1}]; a(2)=2: [{12}], [{2},{1}]; a(3)=8: 
               [{123}], [{2},{13}], [{3}, {12}], [{23}, {1}], [{13},{2}], [{2},{3},
               {1}], [{3},{1},{2}], [{3},{2},{1}]
%e A095989 atomic preference functions a(1) = 1: 1; a(2)=2: 11, 21; a(3)=8: 111, 
               212, 221, 211, 121, 312, 231, 321
%p A095989 A000670 := proc(n) option remember; local k; if n <=1 then 1 else add(binomial(n,
               k)*A000670(n-k),k=1..n); fi; end: add(A000670(k)*x^k,k=0..20): series(1-1/
               %,x,21): [seq(coeff(%,x,i),i=1..20)];
%Y A095989 Cf. A000670, A074664, A095993.
%Y A095989 Sequence in context: A085615 A054726 A003576 this_sequence A124453 A000165 
               A109664
%Y A095989 Adjacent sequences: A095986 A095987 A095988 this_sequence A095990 A095991 
               A095992
%K A095989 nonn
%O A095989 1,2
%A A095989 Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Jul 18 2004